My hosting service doesn't provide easy access to raw log files. Add-ons such as those provided by JetPack require that your site access other, external sites to update stats. If there is any problem with those sites, it can lead to a totally unacceptable response time for your site. (JetPack slowed my site load time from under 1 second to as much as 10 or 15 seconds for at least a few hours one day! Not acceptable!)

By keeping log files local (on your site), you don't need to worry about that external access time issue. Yes, you give up the "real-time" update of the stats, and all the pretty "bells and whistles" provided by those other add-ons. But by analyzing the logs in a "batch" mode, such as weekly or monthly (rather than every access as with "real-time"), you can greatly reduce the potential for performance degradation on your site. And the stats provided by these "old school" tools are perfectly acceptable in many cases.

Plus, the raw log files allow you to perform better forensic investigation after a "hack," whereas those other stat packages tend to show aggregated statistics, hits, etc. If you want to know who accessed what file at a particular time on a particular date, the raw files will be of much more help.

Of course, this does require that you have the ability to analyze the raw log files yourself. In my case, I use good ol' Webalizer and similar tools to provide weekly and/or monthly stats. Until I "need" the fancier stats, and until I "need" it in real-time, I'm happy to keep my WP-based sites responsive!

Webalizer is native on Linux (GPL open license), but there are Windows ports if you need them. I haven't tried those ports.

Pros:

Possibly improved site performance (a big pro!)

Raw files can be analyzed "seven ways to Sunday"

Greatly improved ability to investigate attacks.

Warm, fuzzy feeling knowing you're keeping "old school" alive

Cons:

Stats are not real-time

Lack of "bells and whistles" that other add-ons have

Requires you to manually install and run analysis tools

No direct access from within WP Admin area

Bottom line: even though this plugin "has not been updated for over 2 years", it still has life and still serves a useful purpose. If you are using any of the fancier logging/stat add-ons and experiencing performance issues, or if you think you might ever need to track down how your site got hacked, you should seriously consider this plugin!